Articles by two American mathematicians, E. V. Huntington and Oswald Veblen, are discussed as examples of a movement in foundational research in the period 1900-1930 called American postulate theory. This movement also included E. H. Moore, R. L. Moore, C. H. Langford, H. M. Sheffer, C. J. Keyser, and others. The articles discussed exemplify American postulate theorists' standards for axiomatizations of mathematical theories, and their investigations of such axiomatizations with respect to metatheoretic properties such as independence, completeness, and (...) consistency. (shrink)

Articles by two American mathematicians, E. V. Huntington and Oswald Veblen, are discussed as examples of a movement in foundational research in the period 1900-1930 called American postulate theory. This movement also included E. H. Moore, R. L. Moore, C. H. Langford, H. M. Sheffer, C. J. Keyser, and others. The articles discussed exemplify American postulate theorists' standards for axiomatizations of mathematical theories, and their investigations of such axiomatizations with respect to metatheoretic properties such as independence, completeness, and (...) consistency. (shrink)

Topology uses simple geometric and algebraic ideas, but its huge success and vast ramifications make it a tough nut for historians of twentieth‐century mathematics. Two books have addressed it well: Dieudonné chronicles about one thousand key definitions and theorems, and essays in James focus on forty central themes. Both assume considerable mathematics, but neither offers a historical synthesis of the simplest core ideas. Now, Alain Herreman uses semiotics to watch these leading ideas develop through the founding works of Henri Poincaré, (...) Oswald Veblen, James Alexander, and Solomon Lefschetz. Herreman states outright that semiotics will not exhaust these meanings, but he makes it a revealing tool.The method is especially suited to Poincaré, who will define one technical term repeatedly in a single work, each time differently, as if it was the first, and perhaps no definition will match any use of the term in proofs. For Poincaré no term gets meaning from a definition. Each functions in relation to the others—that is, specifically in relation to other terms in Poincaré's work. It is no use invoking standards of rigor current in Poincaré's time and place or then‐current definitions. Poincaré was well known at the time for using neither: Poincaré's meanings must be derived from his writing, as Herreman does.Herreman bases his semiotics on Hjelmslev yet refutes Hjelmslev's concern that mathematics may be “monoplanar,” with no content beyond the signs themselves . The book depicts four levels of content at work in these authors: algebraic, geometric, arithmetic, and set theoretic. Herreman says a sign has algebraic content if its use depends on its written expression, the way polynomials are formal expressions added and multiplied by formal rules. Early topologists—here especially Alexander—sought purely combinatorial methods. Thus a “cube” is a set of six “faces,” twelve “edges,” and eight “vertices,” each taken as primitive and described only by a short table showing which ones meet which. Combinatorics typifies arithmetic content for Herreman. Yet a cube is also an infinite set of points. Herreman speaks of geometric content when a sign indicates both a set of parts and a set of points. Today we might use different notations for the set of points and the set of parts—Poincaré et al. did not. Herreman will not reconstruct their works or restate them in other words; rather, he uses these levels of content to organize extensive quotations and analyze the relations in each text as they move toward deeper union of the algebraic and geometric.The chapter on Lefschetz makes a great finale. Lefschetz is arguably Poincaré's closest and greatest student, though the two never met. Like Poincaré's, his work is at once compelling and baffling, decisive for the future of mathematics yet brutally difficult to absorb. Semiotics serves well in presenting this mathematician who “never stated a false theorem or gave a correct proof,” as his friends joked.The book does not go far into theorems. Yet it requires some background. A beginner might enjoy it with Alexandroff , a gem itself, written with unusually strong historic sense. Specialists will enjoy reading it with the original works for its fresh viewpoints and novel connections. It is a fine way to analyze the works, to see how they create their own meanings. (shrink)

What is philosophy about and what are its methods? _Philosophy and Ordinary Language_ is a defence of the view that philosophy is largely about questions of language, which to a large extent means _ordinary_ language. Some people argue that if philosophy is about ordinary language, then it is necessarily less deep and difficult than it is usually taken to be but Oswald Hanfling shows us that this isn't true. Hanfling, a leading expert in the development of analytic philosophy, covers (...) a wide range of topics, including scepticism and the definition of knowledge, free will, empiricism, folk psychology, ordinary versus artificial logic, and philosophy versus science. Drawing on philosophers such as Austin, Wittgenstein, and Quine, this book explores the nature of ordinary language in philosophy. (shrink)

Peter Abelard (1079–1142 ce) was the most wide‐ranging philosopher of the twelfth century. He quickly established himself as a leading teacher of logic in and near Paris shortly after 1100. After his affair with Heloise, and his subsequent castration, Abelard became a monk, but he returned to teaching in the Paris schools until 1140, when his work was condemned by a Church Council at Sens. His logical writings were based around discussion of the “Old Logic”: Porphyry's Isagoge, aristotle'S Categories and (...) On Interpretation and boethius'S textbook on topical inference. They comprise a freestanding Dialectica (“Logic”; probably c.1116), a set of commentaries (known as the Logica [Ingredientibus], c. 1119) and a later (c. 1125) commentary on the Isagoge (Logica Nostrorum Petititoni Sociorum or Glossulae). In a work Abelard called his Theologia, issued in three main versions (between 1120 and c.1134), he attempted a logical analysis of trinitarian relations and explored the philosophical problems surrounding God's claims to omnipotence and omniscience. The Collationes (“Debates,” also known as “Dialogue between a Christian, a Philosopher and a Jew”; probably c.1130) present a rational investigation into the nature of the highest good, in which the Christian and the Philosopher (who seems to be modeled on a philosopher of pagan antiquity) are remarkably in agreement. The unfinished Scito teipsum (“Know thyself,” also known as the “Ethics”; c.1138) analyses moral action. (shrink)

This book is a compact, accessible treatment of the main ideas advanced by the positivists, including Schlick, Carnap, Ayer, and the early Wittgenstein. Oswald Hanfling discusses such ideas as the 'verification principle' ('the meaning of this statement is the method of its verification') and the 'elimination of metaphysics, ' an attempt to show that metaphysical statements, for example about God, are unverifiable and therefore meaningless.

At the time of its initial publication in 1904, The Higher Learning in America was known in educated circles as the most reflective study ever made of the university system in America. Veblen's evaluation of the misleading notions and erroneous beliefs were inherent in "the higher learning" was received as fair by most academics. As a result, many believed he paved the way to an improved age in college education.Just as applicable today as they were decades ago, his sophisticated (...) style remains deprecatingly amusing; his biting critique just as disquieting as it was at the turn of the 19th century. The Higher Learning in America remains a penetrating book by one of America's greatest social critics.American economist and sociologist THORSTEIN BUNDE VEBLEN (1857-1929) was educated at Carleton College, Johns Hopkins University and Yale University. He coined the phrase "conspicuous consumption." Among his most famous works are The Theory of the Leisure Class (1899), The Theory of Business Enterprise (1904), and Imperial Germany and the Industrial Revolution (1915). (shrink)

In diesem Aufsatz geht der Autor der Frage nach, ob und in wiefern die theologische Annahme, daß das Christusgeschehen paradigmatisch für den Begriff des Handeln Gottes ist, verständlich ist. Der Verfasser analysiert dafür die Geschichte der Leben-Jesu-Forschung und versucht die christologischen Konsequenzen der verschiedene Interpretationen für die Konstruktion eines Modells des Handeln Gottes herauszufinden. Er benützt Gedanken geschichtsphilosophischer Art um eine solche Ausdehnung der Vorstellung des Christusgeschehens zu verteidigen, daß auch andere Zeiten als das erste Jahrhundert einzuschließen sind. Damit zeigt (...) der Verfasser, daß Lessings Problem des garstigen Grabens und viele Formen der Leben-Jesu-Forschung theologisch von falschen Fragestellungen ausgehen. (shrink)

Name der Zeitschrift: Neue Zeitschrift für Systematische Theologie und Religionsphilosophie Jahrgang: 57 Heft: 1 Seiten: 138-154.

Wittgenstein's later writings generate a great deal of controversy and debate, as do the implications of his ideas for such topics as consciousness, knowledge, language and the arts. Oswald Hanfling addresses a widespeard tendency to ascribe to Wittgenstein views that go beyond those he actually held. Separate chapters deal with important topics such as the private language argument, rule-following, the problem of other minds, and the ascription of scepticism to Wittgenstein. Describing Wittgenstein as a 'humanist' thinker, he contrasts his (...) views on language, art humanity and philosophy itself with those of scientifically minded philosophers. He argues that 'the human form of life' calls for a kind of understanding that cfannot be achieved by the methods of emirical science; that consiousness, for example, cannot properly be regarded as a property of the bran; and that the resulting 'problem of consoiusness is an illusion. Wittgenstein and the Human Form of Life is essential reading for anyone interested in Wittgenstein's approach to what it means to be human. It will be invaluable to all Wittgenstein scholars, and all who are interested in the philosophy of mind, language and aesthetics. (shrink)

In modern representative democracies, much healthcare is publicly funded or provided and so the question of what healthcare systems should do is a matter of public policy. Given that public resources are inevitably limited, what should be done and who should benefit from healthcare? It is a dilemma for policymakers and a subject of debate within several disciplines, but rarely across disciplines. In this paper, I draw on thinking from several disciplines and especially philosophy, economics, and systems theory. I conclude (...) that economist and philosopher John Broome’s writing provides the framework for an answer: a healthcare system in a democracy should do as much good as possible, although sometimes we should sacrifice some overall good for the sake of fairness. This leaves open some detailed questions about what in practice we consider to be good and fair, and about when some good should be traded off in order to be fair. The answers to these questions depend on our values, or as explained by systems theory, our weltanschauung. How policy decisions should be made when citizens’ values differ is a subject of extensive academic debate. However, it is a separate question. Representative democracies have mechanisms for resolving such debates. (shrink)

La comparaison, trop commode, du langage avec un code amène à penser que la fonction fondamentale de la communication linguistique est la transmission d'informations. On est alors conduit à croire que tout ce qui est dit l'est au même titre, avec le même statut d'assertion. En fait, les diverses indications qu'apporte un acte d'énonciation se situent souvent à des niveaux tout à fait différents. Il y a ce dont on entend explicitement informer l'auditeur, mais il y a aussi ce qu'on (...) présente comme un acquis indiscutable dont on fait le cadre du dialogue. Et il y a enfin ce qu'on laisse à l'auditeur le soin de deviner, sans prendre la responsabilité de l'avoir dit. Une sémantique qui s'en tiendrait au niveau de l'explicite serait totalement artificielle : elle rendrait incompréhensible le discours, l'activité effective accomplie au moyen de la parole. Mais surtout, elle défigurerait la langue elle-même ; c'est en effet un trait inhérent à la langue, et l'un de ses traits les plus constants et les plus fondamentaux, que de permettre aux interlocuteurs d'instituer entre eux un réseau de rapports implicites. (shrink)

Ernst Cassirer wird in diesem Buch als ein Denker vorgestellt, der geistig in der philosophischen Tradition wurzelt und sich gleichzeitig den Herausforderungen duch die europäische Moderne stellt: dem Festschreiben eines vor allem durch die Wissenschaften beglaubigten universalen Vernunftanspruchs auf der einen und der Anerkennung einer Vielfalt kultureller Welten auf der anderen Seite. Über die Analyse einiger Grundbegriffe des Cassirerschen Entwurfs einer "Philosophie der symbolischen Formen" - in die auch die Werke aus dem Nachlass Cassirers miteinbezogen werden - versucht der Autor, (...) die Spannungen sichtbar zu machen, die diesem Entwurf die Modernität geben und ihn offen machen für eine Weiterentwicklung. "Die Vielfalt der symbolischen Welten und die Einheit des Geistes", "der Werkbegriff im Denken Cassirers", "Ausdruck und symbolische Prägnanz", "die ethische Dimension des symbolischen Handelns", "das Denken der Renaissance und die Wurzeln der Moderne", sind die Titel, unter denen - von einer bestimmten Seite aus - jeweils ein Blick auf das Ganze des Cassirerschen Denksn gewonnen werden soll. Dass dieses Ganze kein geschlossenes "System" sein, sondern Wege zum Verstehen unserer geistigen und kulturellen SDituation freilegen will, zeigt der Autor in einer abschließenden Analyse, die auch die Bedeutung des Cassirerschen Entwurfs für die philosophische Diskussion der Gegenwart darzulegen versucht. (shrink)

“Articulate models” subservient to formal intelligence are imagined to be heterarchies of automata capable of performing the “symbolic (quasi-spatial) syntheses” of Luria (1973), where “quasi-spatial” points to the abstract core of spatiality: the symbol productions, combinations, and substitutions of algebraic reckoning. The alleged cognitive role of internal “topographic images” and of “efference copies” is confronted with this background and denied.

Asked about Wittgenstein's contribution to aesthetics, one might think first of all of his discussion of ‘family resemblance’ concepts, in which he argued that the various instances of games, for example, need not have any feature or set of features in common, in virtue of which they are all called games; the concept of a game can function perfectly well without any such set of conditions. This insight was soon applied to the much debated quest for a definition of the (...) word ‘art’, and it was claimed that here too the various instances of art were related by way of family resemblance, so that it was futile to look for a condition or set of conditions, which works of art, and only works of art, had in common. Wittgenstein himself did not extend his argument to the concept of art. Although he was deeply interested in the arts, especially music, he wrote very little on aesthetics, his most sustained treatment of the topic being available for us only in the form of notes taken of a set of his lectures on aesthetics. (shrink)

I consider and reject two kinds of solution of the problem of feelings about fictional objects: that the relevant beliefs are not really different as between fiction and fact; and that the relevant feelings are not 'really the same'. The problem should be seen in the context of different phases in acquiring the relevant feeling-concepts and I distinguish three such phases. The first is necessarily 'presentational': the child is presented with suitable objects or pictures and responds with appropriate feelings, without (...) distinguishing fact from fiction. This presentational phase remains part of the concept and our responses to fictional objects should be understood accordingly. (shrink)

Life and Meaning surveys a variety of Philosophical answers to the question, 'What makes life worth living?' By collecting readings from a wide range of philosophical history it gives the various perspectives on the value and meaning of life. Aspects of life which appear to make it meaningless 9death, suffering, randomness) are seen in the light of their long and varied history in philosophical literature and are subjected to careful scrutiny. The texts chosen here pose these and related issues and (...) offer various responses. By careful selection and helpful editorial introduction Life and Meaning gives essential texts which provide the background to contemporary enquiries. Is self-realization a coherent ideal? Does it mean being true to our original nature or to our potential as 'rational animals'? Should we live according to our desires and in pursuit of happiness? Should we appeal to a nature or 'essence' be rejected as bad faith? (shrink)